It is well known in the art that, if the intake port (the opening of an intake passage) of a two-cycle engine is enlarged, the intake efficiency can be increased to improve the engine performance. However, an inherent limit exists in the area of the piston sliding wall of the cylinder. The intake, scavenging and exhaust ports are opened and closed by the piston so that the opening and closing timings (i.e., port timings) are dependent upon the area, shape and position relationships of those ports and therefore these exert heavy influences upon the engine performance. Therefore, it is difficult to enlarge the intake port to an arbitrary extent. Especially in order to enlarge the intake port while properly maintaining the port timings, the intake port has to be enlarged in the circumferential direction of the piston sliding wall of the cylinder. In this situation, the area of the sliding wall receiving the piston is accordingly reduced. As a result, the piston, which is liable to be forced into contact with the intake port when it is shifted to its rising stroke from the bottom dead center, will be tilted, generally speaking, with the resultant drawbacks that the piston has its skirt portion abutting against the edge portion of the intake port thereby to generate rattling noises, and that the sliding resistance is increased thereby to increase the power loss. Therefore, such means has not been employed.